Details

sample133.0ms

Algorithm

intervals

Results

62.0ms	71×	body	10240	exit
44.0ms	270×	body	80	valid
4.0ms	9×	body	320	valid
3.0ms	3×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	4×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	24
3	24
2	20
1	13
0	8

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.5b	(log1p (exp x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-neg` `prod-diff`
2×	`pow1` `log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--`

Counts

2 → 34

Calls

2 calls:

9.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series170.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (log1p (exp x)) (* y x))
82.0ms	(log1p (exp x))

simplify2.0s

Counts

40 → 40

Iterations

Iter	Nodes
4	2334
3	953
2	314
1	126
0	61

prune379.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(log1p (exp x))
0.5b	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))
0.7b	(sqrt (log1p (exp x)))
0.7b	(sqrt (log1p (exp x)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
5×	`expm1-log1p-u`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`log1p-udef` `log1p-expm1` `fma-udef`

Counts

4 → 55

Calls

4 calls:

0.0ms	(log1p (exp x))
0.0ms	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))
1.0ms	(sqrt (log1p (exp x)))
1.0ms	(sqrt (log1p (exp x)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(log1p (exp x))
193.0ms	(fma (sqrt (log1p (exp x))) (sqrt (log1p (exp x))) (- (* y x)))
96.0ms	(sqrt (log1p (exp x)))
110.0ms	(sqrt (log1p (exp x)))

simplify3.7s

Counts

67 → 67

Iterations

Iter	Nodes
5	6131
4	1793
3	654
2	262
1	132
0	76

prune799.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
0.0b	(fma x (fma x 1/8 1/2) (log 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

2 → 33

Calls

2 calls:

12.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
1.0ms	(fma x (fma x 1/8 1/2) (log 2))

series111.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))
52.0ms	(fma x (fma x 1/8 1/2) (log 2))

simplify9.0s

Counts

39 → 39

Iterations

Iter	Nodes
4	8606
3	1766
2	343
1	130
0	59

prune345.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (* (exp (* (fma 1/8 x 1/2) x)) 2)) (* y x))
0.0b	(* (fma 1/8 x 1/2) x)
0.0b	(exp (* (fma 1/8 x 1/2) x))
0.3b	(log (* (exp (* (fma 1/8 x 1/2) x)) 2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
7×	`add-log-exp`
6×	`add-cbrt-cube` `log-pow`
5×	`fma-neg` `prod-diff`
4×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `associate-l`
2×	`log-prod` `rem-log-exp` `prod-exp`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr` `rem-exp-log`

Counts

4 → 75

Calls

4 calls:

51.0ms	(- (log (* (exp (* (fma 1/8 x 1/2) x)) 2)) (* y x))
6.0ms	(* (fma 1/8 x 1/2) x)
4.0ms	(exp (* (fma 1/8 x 1/2) x))
18.0ms	(log (* (exp (* (fma 1/8 x 1/2) x)) 2))

series262.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (log (* (exp (* (fma 1/8 x 1/2) x)) 2)) (* y x))
77.0ms	(* (fma 1/8 x 1/2) x)
19.0ms	(exp (* (fma 1/8 x 1/2) x))
85.0ms	(log (* (exp (* (fma 1/8 x 1/2) x)) 2))

simplify1.4s

Counts

87 → 87

Iterations

Iter	Nodes
3	3315
2	744
1	245
0	112

prune764.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes74.0ms

Accuracy

0% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
3	15
2	15
1	13
0	8

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.0s	2358×	body	10240	exit
1.1s	8435×	body	80	valid
119.0ms	212×	body	320	valid
111.0ms	233×	body	640	valid
96.0ms	118×	body	1280	valid
48.0ms	120×	body	160	valid